标题： Q张量梯度流的极大值界原理与低正则性积分器 显示英文标题

标题： Maximum bound principle for Q-tensor gradient flow with low regularity integrators

摘要： 我们研究用于描述向列相液晶半线性抛物方程的Q张量模型的低正则性积分器（LRI）方法。 使用杜哈梅尔公式开发了一阶和二阶时间离散化，并严格证明了在最小正则性要求下，这两种方案都保持最大值界限原理（MBP）和能量耗散。 建立了所提出方法的最佳收敛速率。 数值实验验证了理论结果，表明Q的特征值始终严格限制在物理范围内（-1/3, 2/3）。 显示英文摘要

摘要： We investigate low-regularity integrator (LRI) methods for the Q-tensor model governing nematic liquid-crystalline semilinear parabolic equation. First- and second-order temporal discretizations are developed using Duhamel's formula, and we rigorously prove that both schemes preserve the maximum bound principle (MBP) and energy dissipation under minimal regularity requirements. Optimal convergence rates are established for the proposed methods. Numerical experiments validate the theoretical findings, demonstrating that the eigenvalues of Q remain strictly confined within the physical range (-1/3},2/3).